For those who’ve been around the Capitol a while, one face is surging especially fast into view as Donald Trump describes what he’s looking for in a vice president.

The presumptive Republican nominee says he’ll very likely want someone with much more traditional experience in politics and public service than his — a person who would command immediate attention in Congress, be skilled at shaping and advancing a legislative program, be a partner in governing and be prepared to become a worthy president at a moment’s notice.

[Related: The Veep Trump Needs But Won't Get] Newt Gingrich is among a very few prominent figures who not only readily fits all those criteria, but also sounds eager to be asked and could actually help Trump’s chances in November. As recently as Friday, Gingrich told a local television station he would "listen carefully" if Trump suggested he join the ticket.

The former speaker of the House was an avatar of today’s confrontational conservatism, but he nonetheless negotiated some of the biggest bipartisan deals of the 1990s. His ability to sell himself as both career insurgent and inside player sustained a serious run for president four years ago. His standing in both the Washington establishment and with the elite on the right would allow him to raise many millions of dollars for the fall campaign.

[Related: Trump's Best Move: Kasich for VP] A truism of modern politics is that the first genuinely presidential-caliber decision a nominee makes is choosing a running mate. In some of his rare moments of self-critical reflection, Trump himself has volunteered he needs to “start acting more presidential.” That suggests he understand he can’t afford to make a pick that magnifies the considerable worries undecided voters have about his broad range of over-the-top behavior.

It’s also become conventional wisdom that a fine choice for No. 2 won’t help as much as a poor choice will hurt. Ideology aside, very few questioned the presidential qualifications of the elder George Bush or John McCain, and yet Dan Quayle became a drag on the 1988 GOP ticket and Sarah Palin helped cost the party the White House in 2008.

Finally, the old expectations that a running mate should provide demographic or ideological balance have been supplanted by a different priority — creating a pairing of the personally compatible.

Gingrich fits the bill on all fronts. His leadership of the House put him two heartbeats from the presidency from 1995 through 1998. He’s remained one of the Republican right’s most prominent faces, idea generators and diversified experts on policy ever since, so his selection wouldn’t engender any “Who’s he?” head-scratching. His combative campaign tactics and revolution-stoking rhetorical tropes complement the approaches of the combustible nominee.

Gingrich’s rising to the top of Trump’s short list assumes a deliberative and exhaustive vetting process beginning very soon and run by someone other than the candidate, with insider’s experience. It further assumes a decision early on against elevating some charismatic but relatively untested person to the top flight of American politics, even if doing so would provide the ticket with enticing gender or ethnic balance or put a swing state in reach.

Fortunately for today’s Republican Party, however, it has a very deep bench of already viable national leaders. Unfortunately for Trump, a whole lot of those people have very sound reasons for wanting to steer clear of the GOP’s putative new boss.

John Kasich, Marco Rubio, Scott Walker, Lindsey Graham and Jeb Bush all retain solid followings and credentials — geographic, experiential and ideological — making them obvious potential running mates . But all have gone way beyond the customary demurrals and expressed emphatic disinterest in being considered. Their rationales include the sting of Trump’s campaign brickbats remaining too sharp to ignore so soon, or worry that their own future aspirations would be hobbled by an uphill and losing run for national office this time.

Trump would stand to benefit by picking a woman to help tackle his yawning gender gap, so maybe ruling out those 2016 rivals isn’t such a bad idea. But wooing a Republican female with unambiguous presidential stature will be difficult.

Kelly Ayotte of New Hampshire, who made Mitt Romney’s long list in 2012, looks unwilling to effectively trade away her shot at a second Senate term in New Hampshire. Former Secretary of State Condoleezza Rice appears unready to join her fortunes to someone who’s so forcefully insulted the Bushes who cultivated her career. The two most prominent female governors, Nikki Haley of South Carolina and Susana Martinez of New Mexico, would have to struggle to walk back their criticism of Trump’s angry and misogynistic rhetoric.

All this has quickly reduced the most obvious initial short list to a handful of prominent figures who haven’t backed away from getting name-checked in the early speculation. But from that roster it’s probably safe to drop Ben Carson, who remains a tea party conservative favorite but has none of the governing partner credentials Trump says he wants.

[Strickland Hits Portman for Over Trump VP Consideration] This leaves three second-term governors — Rick Scott of all-important Florida, former House Armed Services member Mary Fallon of Oklahoma and fellow rhetorical warrior Chris Christie of New Jersey — with arguably less political baggage than potential benefit. Also on the list is Jeff Sessions of Alabama , the first senator to endorse Trump and a conservative policy-making veteran on the Judiciary, Armed Services and Budget committees.

But Gingrich looks like the best fit of them all. His “Contract with America” campaign of 1995, which won the House for the GOP for the first time in 40 years, demonstrated his ability to redirect the national political conversation.

His successful drives to revamp the welfare system and balance the budget showed he could forge consensus on enormously important issues while still pillorying his Democratic bargaining partners. His deep familiarity with the Clintons from those years can’t help but be valuable now.

If there’s an early knock against Gingrich inside the GOP, it’s that he’s been too sycophantically enthusiastic about the billionaire’s business acumen and political skill. Although he made no endorsement during the contested primaries, behind closed doors Gingrich touted Trump’s virtues to Washington insiders long before it was clear he’d be the nominee.

And if the ticket comes to fruition, Democrats will surely delight in mocking a pair of three-times married, puffed up, aging white guys with surreal hair and more talent for making bombastic pronouncements than for shaping public policy.

Look for a decision as soon as five weeks from now. Trump will turn 70 on June 14 and Gingrich celebrates his 73rd birthday three days later.